Inverse Lyapunov Approach for semi-active control of civil structures

Abstract

In the present paper an Inverse Lyapunov method in a bang-bang type semi-active control for civil structures is proposed. The vibration control device (VCD) that has been developed by authors is employed for the semi-active control. The VCD is installed between two neighboring stories of structures like general dampers and generates two types of resistance forces, i.e. an inertial force proportional to the relative acceleration and a damping force proportional to the relative velocity of the two floors. The damping coefficient of the VCD can be changed by a command signal to an electric circuit connected to the VCD. In conventional Lyapunov-based semi-active control the Lyapunov function is firstly determined, mostly it is defined as the sum of the kinetic and potential energies at every instant, and the bang-bang type control is derived so that the dissipation rate of the defined Lyapunov function (the total energy) is maximized. In this paper, conversely, we assume the simple bang-bang type control firstly and then the Lyapunov function is searched so that the high performance on vibration suppression of civil structures, e.g. small relative displacement between adjacent two floors and absolute acceleration of each storey, etc., is achieved. Genetic Algorithm is adopted for the search of the Lyapunov function. Structural responses subject to recorded and artificial earthquake waves are used in the searching process. We show the effectiveness of the proposed Inverse Lyapunov Approach with a simulation example for a 15-storey building with three VCDs. Copyright © 2010 John Wiley & Sons, Ltd.